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4. Pet Palace: Reporting results of division as fractions (A)
Lesson objective: Solve problems involving fair share situations to practice reporting fractional remainders.
This lesson provides an opportunity for students to apply their knowledge and understanding of interpreting fractional remainders in a fair share situation to a reallife situation. Students are asked to create a list for the new owners of Pet Palace telling them how to evenly share the supplies left for the cats and kittens.
Key Concept students will use:

We can interpret \(({a \over b}) \times q\) as "a" parts of a partition of q into b equal parts.
Skills students will use:
 interpret quotients of whole numbers as a number of shares and a number of groups. (Grade 3, Unit 7, 3.OA.1.2)
 use drawings and equations to represent and solve division situational problems involving equal groups. (Grade 3, Unit 7, 3.OA.1.2)
Students engage in Mathematical Practice 8 (Look for and express regularity in repeated reasoning) as they use solve a variety of similar situations that require them to express a remainder as a fairly shared amount.
Key vocabulary:
 denominator: the number of equalsize parts into which the whole has been partitioned. For example, in the fraction \(3 \over 8\), 8 is the denominator. The denominator is written below the horizontal bar in a fraction. It is also the divisor.
 dividend: the name for the number into which you are dividing in a division problem. For example, 36 is the dividend in the equation 36 ÷ 4 = 9.
 division: A mathematical operation based on sharing or separating into equal parts.
 divisor: the name for the number that divides another number. For example, in the equation 36 ÷ 4 = 9, the divisor is 4.
 equal: exactly the same in value
 fractional remainder: the amount left over when values are divided into equal shares, expressed as a fraction. In the division equation 16 ÷ 3 = 5 R1 the remainder is 1, which can also be expressed as \(1 \over 3\).
 numerator: the number of equal parts being considered. For example, in the fraction \(3 \over 8\), 3 is the numerator. The numerator is written above the horizontal bar in a fraction. It is also the dividend.
 quotient: The result of dividing one number by another number. For example, in the equation 36 ÷ 4 = 9, the quotient is 9.
 remainder: The amount left over when values are divided into equal shares. In the division equation 16 ÷ 3 = 5 R1 the remainder is 1.